In TPWeb CP you have a few different configuration options.
Location:
/usr/local/vesta/conf/vesta.conf
Content:
WEB_SYSTEM='httpd'
WEB_RGROUPS='apache'
WEB_PORT='8080'
WEB_SSL_PORT='8443'
WEB_SSL='mod_ssl'
PROXY_SYSTEM='nginx'
PROXY_PORT='80'
PROXY_SSL_PORT='443'
DNS_CLUSTER='yes'
STATS_SYSTEM='webalizer,awstats'
FTP_SYSTEM='vsftpd'
DNS_SYSTEM='named'
MAIL_SYSTEM='exim'
ANTIVIRUS_SYSTEM='clamav'
ANTISPAM_SYSTEM='spamassassin'
IMAP_SYSTEM='dovecot'
CRON_SYSTEM='crond'
FIREWALL_SYSTEM='iptables'
FIREWALL_EXTENSION='fail2ban'
BACKUP_SYSTEM='sftp,local'
LANGUAGE='en'
VERSION='0.0.24'
LETSENCRYPT='yes'
DB_SYSTEM='mysql'
API='yes'
As you can see, the most of the settings are set at installation, to know what kind of setup you have installed. The most important option that is changeable for you is the API option. With this option you can enable or disable the web api. By default this option is disabled.